They both do the same job, they just do it differently. An active crossover filters a line-level signal based on the incoming frequency bands. It operates as a preamp, and a separate amplifier channel is required for each pass-band output (i.e. one amp for the woofer, one amp for the midrange, one amp for the tweeter on each side.) A passive crossover operates as a speaker-level filter to control what frequency bands are reproduced by each speaker in a system. It requires one amplifier channel per speaker system and it can be custom tailored to precisely match two or more specific speakers. Both types will color and change the quality of the sound. Passive crossovers consume some amplifier power and generate some heat to do their job. An active crossover does not consume amplifier power and it can allow better dynamic range and power utilization in a well-designed system, although it is much more difficult to set up and to get the proper level matches between speaker components than is a passive-based system, it is generally a much more expensive approach (because of the multiple amplifiers that must be used) and it adds a lot of complexity to a system. An active crossover is however a far better approach for a subwoofer crossover.
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